// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.

#ifndef EIGEN_EULERANGLES_H
#define EIGEN_EULERANGLES_H

namespace Eigen {

/** \geometry_module \ingroup Geometry_Module
 *
 *
 * \returns the Euler-angles of the rotation matrix \c *this using the convention defined by the triplet (\a a0,\a a1,\a
 * a2)
 *
 * Each of the three parameters \a a0,\a a1,\a a2 represents the respective rotation axis as an integer in {0,1,2}.
 * For instance, in:
 * \code Vector3f ea = mat.eulerAngles(2, 0, 2); \endcode
 * "2" represents the z axis and "0" the x axis, etc. The returned angles are such that
 * we have the following equality:
 * \code
 * mat == AngleAxisf(ea[0], Vector3f::UnitZ())
 *      * AngleAxisf(ea[1], Vector3f::UnitX())
 *      * AngleAxisf(ea[2], Vector3f::UnitZ()); \endcode
 * This corresponds to the right-multiply conventions (with right hand side frames).
 *
 * The returned angles are in the ranges [0:pi]x[-pi:pi]x[-pi:pi].
 *
 * \sa class AngleAxis
 */
template<typename Derived>
EIGEN_DEVICE_FUNC inline Matrix<typename MatrixBase<Derived>::Scalar, 3, 1>
MatrixBase<Derived>::eulerAngles(Index a0, Index a1, Index a2) const
{
	EIGEN_USING_STD(atan2)
	EIGEN_USING_STD(sin)
	EIGEN_USING_STD(cos)
	/* Implemented from Graphics Gems IV */
	EIGEN_STATIC_ASSERT_MATRIX_SPECIFIC_SIZE(Derived, 3, 3)

	Matrix<Scalar, 3, 1> res;
	typedef Matrix<typename Derived::Scalar, 2, 1> Vector2;

	const Index odd = ((a0 + 1) % 3 == a1) ? 0 : 1;
	const Index i = a0;
	const Index j = (a0 + 1 + odd) % 3;
	const Index k = (a0 + 2 - odd) % 3;

	if (a0 == a2) {
		res[0] = atan2(coeff(j, i), coeff(k, i));
		if ((odd && res[0] < Scalar(0)) || ((!odd) && res[0] > Scalar(0))) {
			if (res[0] > Scalar(0)) {
				res[0] -= Scalar(EIGEN_PI);
			} else {
				res[0] += Scalar(EIGEN_PI);
			}
			Scalar s2 = Vector2(coeff(j, i), coeff(k, i)).norm();
			res[1] = -atan2(s2, coeff(i, i));
		} else {
			Scalar s2 = Vector2(coeff(j, i), coeff(k, i)).norm();
			res[1] = atan2(s2, coeff(i, i));
		}

		// With a=(0,1,0), we have i=0; j=1; k=2, and after computing the first two angles,
		// we can compute their respective rotation, and apply its inverse to M. Since the result must
		// be a rotation around x, we have:
		//
		//  c2  s1.s2 c1.s2                   1  0   0
		//  0   c1    -s1       *    M    =   0  c3  s3
		//  -s2 s1.c2 c1.c2                   0 -s3  c3
		//
		//  Thus:  m11.c1 - m21.s1 = c3  &   m12.c1 - m22.s1 = s3

		Scalar s1 = sin(res[0]);
		Scalar c1 = cos(res[0]);
		res[2] = atan2(c1 * coeff(j, k) - s1 * coeff(k, k), c1 * coeff(j, j) - s1 * coeff(k, j));
	} else {
		res[0] = atan2(coeff(j, k), coeff(k, k));
		Scalar c2 = Vector2(coeff(i, i), coeff(i, j)).norm();
		if ((odd && res[0] < Scalar(0)) || ((!odd) && res[0] > Scalar(0))) {
			if (res[0] > Scalar(0)) {
				res[0] -= Scalar(EIGEN_PI);
			} else {
				res[0] += Scalar(EIGEN_PI);
			}
			res[1] = atan2(-coeff(i, k), -c2);
		} else
			res[1] = atan2(-coeff(i, k), c2);
		Scalar s1 = sin(res[0]);
		Scalar c1 = cos(res[0]);
		res[2] = atan2(s1 * coeff(k, i) - c1 * coeff(j, i), c1 * coeff(j, j) - s1 * coeff(k, j));
	}
	if (!odd)
		res = -res;

	return res;
}

} // end namespace Eigen

#endif // EIGEN_EULERANGLES_H
